The bonus stats granted by Awe are not shared with Manamune / Muramana. This means that with Archangel's Staff and Manamune / Muramana you will get both the bonus ability power and attack damage from both items' Awe.

Mana Charge on Tear of the Goddess and Archangel's Staff requires mana expenditure in order to charge, making it impossible for manaless to charge either of those.

On Manamune, on the other hand, manaless champions can charge the mana through basic attacks, until it upgrades to to Muramana. To get Seraph's Embrace, Manamune must provide the stacks while Archangel's Staff takes transformation priority.

On manaless champions, the Awe passive will have no effect whatsoever, and Muramana'sShock will apply but deal no damage.

Strategy

Archangel's Staff is commonly paired with Rod of Ages for many ability power scaling champions. These two items together can effectively eliminate any champion's mana problems and the early Tear of the Goddess and Catalyst of Aeons are useful in lane for the healing sustain and increased mana pool. The only downside to this build is Archangel's Staff / Tear of the Goddess as well as Rod of Ages take considerable time to stack.

Archangel's Staff has great synergy with a Rabadon's Deathcap, as it increases ability power by 40%. This means that whenever your mana is increased, the Archangel's Staff will increase your ability power, and then the Rabadon's Deathcap will increase it again due to the 40% increased ability power passive.

This is equal to 1.4% of the holder maximum mana.

Trivia

Assuming a charge is gained every 4 seconds, the 750 mana charge takes 6 minutes and 15 seconds to max.